Researchers Propose Principled Method for Converting Privacy Parameters in Gaussian Differential Privacy
A new preprint introduces principled mappings from pure differential privacy (ε) to Gaussian differential privacy (GDP) parameter μ, recommending μ ≈ ε/5 as a conservative general-purpose conversion. The work grounds these mappings in worst-case membership inference attack success across three metrics: multiplicative advantage, precision at fixed recall, and the standard privacy profile. This matters because consistent, well-justified parameter choices are essential for accurately reporting and comparing privacy guarantees in machine learning systems.
Submitted to arXiv on June 8, 2026, this preprint by Bogdan Kulynych and colleagues addresses a practical gap in privacy-preserving machine learning: how to translate pure differential privacy guarantees expressed as ε into the Gaussian differential privacy (GDP) framework's μ parameter. The authors derive their mappings by matching the worst-case success of a strong-adversary membership inference attack, evaluated under three distinct metrics to ensure robustness of the recommendation. A tabulation of μ values across a useful range of parameters is provided, culminating in the rule-of-thumb μ ≈ ε/5 for conservative general-purpose use. GDP has gained traction in recent literature as a preferred way to report privacy guarantees because of its analytical tractability and tighter composition properties. By anchoring the conversion in adversarial attack success rather than purely mathematical equivalence, the approach offers a more operationally meaningful basis for practitioners choosing privacy parameters.
What's missing
The paper is a preprint and has not yet undergone peer review. Key open questions include how the recommended μ ≈ ε/5 conversion holds under approximate-DP (δ > 0) settings and how the conversion performs empirically on real-world differentially private training pipelines.
What different sources said
- arXiv cs.LGCenter
On Choosing the $\mu$ Parameter in Gaussian Differential Privacy
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